IC design and verification tools perform Boolean operations on polygonal boundaries of planar regions. For certain applications, however, the use of more general classes of shapes than polygons is required. For example, the shapes of silicon photonics, MEMS, microfluidics devices, and the like may be the result of the mathematical solution of some underlying physical model and therefore most naturally described by curves given by parametric curve functions (mathematical equations) in symbolic form. One way to perform Boolean operations on such boundaries using the existing methods (e.g., complementary metal oxide-semiconductor (CMOS) processes) is by approximating the curved boundaries to polygons. However, the existing methods result in loss of the mathematical information about the positions of various points on a curve, location of intersections of the curve with other curves, tangents and normal to the curve, curvature of the curve, derivative functions of the curve, and the like. Further, it is difficult to reconstruct the original mathematically defined curved boundaries after these have been approximated to polygons.
It is desirable to provide a method and a strategy for performing Boolean operations on mathematically described curved boundaries instead of converting the curved boundaries to polygons.
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